Hmmm - do you have two points occupying the same place? Just go round selecting the points and see if you end up with two rather than the usual one. Alternatively once you've selected all the points just have a look to see how many points you actually have managed to select. You might also want to hunt around adjoining points as well to see if there are points sharing the same space or, indeed if you have any two point polygons in the area. The info window is your friend.
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